What are matrix transformations?

In summary, a matrix represents a linear mapping between vector spaces and can be used to model rotations or reflections. It describes or represents a transformation and can be changed to another matrix through a change of bases.
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Sreekar adithya
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TL;DR Summary
Quick understanding of transformation of an matrix
What does a transformation of a matrix means and how it could be used?
 
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A matrix corresponds to a linear mapping between (finite dimensional) vector spaces. It can for example be used to model rotations or reflections. Here is a video that explains it better than I ever could:

 
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  • #3
Like QED said, repeating because I think it is an important point in avoiding confusion. A matrix describes or represents a transformation, that is what is usually meant by a matrix transformation.
 
  • #4
we might need more info from the OP, as to whether he means the linear transformation defined by the matrix, or the transformation of the matrix, i.e.changing it to some other matrix, defined by a change of bases, say.
 
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1. What is a matrix transformation?

A matrix transformation is a mathematical operation that involves multiplying a matrix by another matrix or vector. This results in a new matrix or vector, which represents the transformation of the original matrix or vector.

2. What are some common examples of matrix transformations?

Some common examples of matrix transformations include scaling, rotation, shearing, and reflection. These transformations can be performed on both 2D and 3D objects, and are commonly used in computer graphics, robotics, and physics.

3. How are matrix transformations used in real-world applications?

Matrix transformations have a wide range of applications in various fields such as computer science, engineering, and physics. They are used to represent and manipulate data, perform calculations, and model real-world systems.

4. What is the difference between a linear and non-linear matrix transformation?

A linear matrix transformation preserves the shape and size of an object, while a non-linear transformation changes the shape and size. In other words, a linear transformation results in a scaled or rotated version of the original object, while a non-linear transformation can result in a distorted or deformed object.

5. How do matrix transformations relate to linear algebra?

Matrix transformations are a fundamental concept in linear algebra, which is the branch of mathematics that deals with linear equations, vector spaces, and matrices. Linear algebra provides the mathematical framework for understanding and performing matrix transformations.

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